THE ELASTOPLASTIC CALCULATION OF FRAMES USING THE DISPLACEMENT METHOD
Journal Title: International Journal for Computational Civil and Structural Engineering - Year 2019, Vol 15, Issue 3
Abstract
We proposed a method for calculating statical indeterminacy frames taking into account plastic deformations, which is based on the use of a schematized diagram of material with hardening. Two types of standard beams with supports are used during the implementation of the displacement method (DM) and the elastic solution of the problem: “fixed” - “pinned” and “fixed” - “fixed”, but unlike the elastic solution, standard beams contain plastic zones (PZs). So as the stresses in these zones did not exceed the limit of yielding in the nonlinear frame calculation, we took measures to transform the PZs into equal strength plastic zones (ESPZ). The calculations were made for both types of beams for all single and load impacts. The frame calculation consists of two stages (elastic and plastic). At the elastic stage, we determine an elastic moment diagram and the corresponding load. For a practical use of the DM in a nonlinear frame calculation, we introduced a simplifying prerequisite supplementing the well-known hypotheses of the classical version of the method, and formulated a Statement of the limiting load. According to the Statement, each length of the PZ can correspond to the lower boundary of the limiting load. The plastic stage of the calculation is performed at a given length of the PZ using the method of sequential loadings. At each loading stage, incremental equations are written using the DM equations, which establish relations between incremental moments and the incremental load, that allows you to get the resulting moment diagram. This diagram represents a sum of the elastic diagram and the diagrams of incremental moments at all previous loading stages. According to the resulting diagram, we calculate the length of the PZ, together with the limiting load. The calculation is considered complete if the length of the PZ does not exceed the specified value within the margin of error.
Authors and Affiliations
Alexander Potapov
Keywords
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- EP ID EP647368
- DOI 10.22337/2587-9618-2019-15-3-120-130
- Views 58
- Downloads 0
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